MEAN FIELD MODELING OF MULTIPHASE SYSTEMS

The theory of multiphase systems was developed at the beginning of the 19th century assuming that different phases are at local equilibrium and are separated by a sharp (i.e. with zero thickness) interface. This approach breaks down when the real interface thickness is comparable to the lengthscale of the phenomenon that is being studied, as it happens near a contact line or in the breakup or coalescence of liquid droplets. A different approach consists in treating the interface as a finite (although thin) region where the density, or the composition, of the mixture varies from one value (not necessarily of equilibrium) to the other. The drawback of this approach is that we have to add a mass conservation equation to the equation of conservation of momentum and of energy, as we need to determine the density (or concentration) profile of the mixture in the interface region. The advantage is that the position of the interface is automatically determined through the concentration profile and so no interface tracking is required. This approach, which is generally referred to as the diffuse interface method, is based on one of the many intuitions by Van der Waals and was later generalized by Ginzburg and Landau to formulate the mean field theory.
After deriving the basic equations of the model, results of several recent simulations are presented and commented. In particular, we will describe spinodal decomposition and nucleation of both liquid binary mixtures and single component, vapor-liquid systems.